The player is ALWAYS deemed to be telling the truth. This is a basic principle of the Rules.
The on-course official is bound by this premise when making a ruling.
So, generally speaking, if it comes down to a simple "he said she said", the ruling would favor the player.

However, an incident such as the one we are discussing, would be taken up by the Committee.
The "Committee" is the person(s) in charge of the tournament.
The Committee has the power to IMPOSE a penalty of disqualification.
The decision of the Committee is FINAL.

The Committee would gather all available evidence in the matter before making a decision.
(For televised events, this would include a review the tapes)

Owing to the seriousness of the result, I would suspect that the Committee would need pretty strong evidence to rule against a players word.
Having said that, Bob Toski "withdrew" from the Senior Tour when tapes showed him repeatedly mis-marking his ball (inchworming).